Showing papers by "Peter Arnold published in 2019"
TL;DR: In this article, a high-energy parton showering as it traverses a QCD medium such as a quark-gluon plasma is considered and the interference effects between successive splittings in the shower are potentially very important but have so far been calculated only in idealized theoretical situations.
Abstract: Consider a high-energy parton showering as it traverses a QCD medium such as a quark-gluon plasma. Interference effects between successive splittings in the shower are potentially very important but have so far been calculated (even in idealized theoretical situations) only in soft emission or large-${N}_{\mathrm{c}}$ limits, where ${N}_{\mathrm{c}}$ is the number of quark colors. In this paper, we show how one may remove the assumption of large ${N}_{\mathrm{c}}$ and so begin investigation of ${N}_{\mathrm{c}}=3$ without soft-emission approximations. Treating finite ${N}_{\mathrm{c}}$ requires (i) classifying different ways that four gluons can form a color singlet and (ii) calculating medium-induced transitions between those singlets, for which we find application of results for the generalization of Wigner $6\text{\ensuremath{-}}j$ symbols from angular momentum to $\mathrm{SU}({N}_{\mathrm{c}})$. Throughout, we make use of the multiple scattering ($\stackrel{^}{q}$) approximation for high-energy partons crossing quark-gluon plasmas, and we find that this approximation is self-consistent only if the transverse-momentum diffusion parameter $\stackrel{^}{q}$ for different color representations satisfies Casimir scaling (even for strongly coupled, and not just weakly coupled, quark-gluon plasmas). We also find that results for ${N}_{\mathrm{c}}=3$ depend, mathematically, on being able to calculate the propagator for a coupled nonrelativistic quantum harmonic oscillator problem in which the spring constants are operators acting on a five-dimensional Hilbert space of internal color states. Those spring constants are represented by constant $5\ifmmode\times\else\texttimes\fi{}5$ matrices, which we explicitly construct. We are unaware of any closed form solution for this type of harmonic oscillator problem, and we discuss prospects for using numerical evaluation.
17 citations
TL;DR: In this paper, it was shown that in-medium splitting rates can be determined in the appropriate limit just from the knowledge of the values of stackrel{^}{q}$ for different color representations.
Abstract: A powerful historical insight about the theory of in-medium showering in QCD backgrounds was that splitting rates can be related to a parameter $\stackrel{^}{q}$ that characterizes the rate of transverse-momentum kicks to a high-energy particle from the medium. Another powerful insight was that $\stackrel{^}{q}$ can be defined (with caveats) even when the medium is strongly coupled, using long, narrow Wilson loops whose two long edges are lightlike Wilson lines. The medium effects for the original calculations of in-medium splitting rates can be formulated in terms of three-body imaginary-valued ``potentials'' that are defined with three long, lightlike Wilson lines. Corrections due to the overlap of two consecutive splittings can be calculated using similarly defined four-body potentials. I give a simple argument for how such $N$-body potentials can be determined in the appropriate limit just from the knowledge of the values of $\stackrel{^}{q}$ for different color representations. For $Ng3$, the $N$-body potentials have a nontrivial color structure, which will complicate calculations of overlap corrections outside of the large-${N}_{\mathrm{c}}$ or soft bremsstrahlung limits.
10 citations
TL;DR: In this article, the authors discuss some possible theorists' tests for simple situations (e.g. an infinite, non-expanding plasma) using thought experiments and first-principles quantum field theory calculations (with some simplifying approximations).
Abstract: High-energy partons (E ≫ T ) traveling through a quark-gluon plasma lose energy by splitting via bremsstrahlung and pair production. Regardless of whether or not the quark-gluon plasma itself is strongly coupled, an important question lying at the heart of philosophically different approaches to energy loss is whether the high-energy partons of an in-medium shower can be thought of as a collection of individual particles, or whether their coupling to each other is also so strong that a description as high-energy “particles” is inappropriate. We discuss some possible theorists’ tests of this question for simple situations (e.g. an infinite, non-expanding plasma) using thought experiments and first-principles quantum field theory calculations (with some simplifying approximations). The physics of in-medium showers is substantially affected by the Landau-Pomeranchuk-Midgal (LPM) effect, and our proposed tests require use of what might be called “next-to-leading order” LPM results, which account for quantum interference between consecutive splittings. The complete set of such results is not yet available for QCD but is already available for the theory of large-Nf QED. We therefore use large-Nf QED as an example, presenting numerical results as a function of Nfα, where α is the strength of the coupling at the relevant high-energy scale characterizing splittings of the high-energy particles.
8 citations
11 Jan 2019
TL;DR: In this article, the effects of non-transverse polarized gauge bosons in the intermediate states and virtual corrections to in-medium splitting rates were calculated for infrared safe calculations of the characteristics of high energy in- medium parton showers.
Abstract: High energy particles such as quarks, gluons, electrons etc. traversing through medium primarily lose energy by showering through hard bremsstrahlung and pair production. These splitting processes are coherent over large distances in the very high energy limit, leading to suppression from the Landau-Pomeranchuk-Migdal (LPM) effect. Avoiding soft-emission approximations, we study the cases where the coherence lengths of two consecutive splittings overlap (which is important for calculating corrections to LPM effect in QCD) and focus on two issues: (i) how to include the effects of non-transverse polarized gauge bosons in the intermediate states, and (ii) how to calculate virtual corrections to in-medium splitting rates, which will be necessary for infrared safe calculations of the characteristics of high energy in-medium parton showers. These in-medium loop calculations require highly non-trivial UV regularization and renormalization. In the current work, we show how to solve these issues for the slightly simpler case of large-Nf QED, where Nf is the number of electron flavors. Finally, we use these results to calculate corrections to in-medium charge stopping length.